A two digit number is obtained by either multiplying sum of digits by 8 and adding 1 or by multiplying the difference of the digits by 13 and adding 2. Find the number.

Explanation

To solve the problem, we need to find a two-digit number based on the given conditions. Let's denote the two-digit number as \(10y + x\), where \(y\) is the digit in the tens place and \(x\) is the digit in the units place.

### Step 1: Set up the equations based on the problem statement.

1. The first condition states that the two-digit number can be obtained by multiplying the sum of its digits by 8 and adding 1:
\[ 10y + x = 8(x + y) + 1 \]
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